Ricci Flow for Shape Analysis and Surface Registration: Theories, Algorithms and Applications
Ricci Flow for Shape Analysis and Surface Registration introduces the beautiful and profound Ricci flow theory in a discrete setting. By using basic tools in linear algebra and multivariate calculus, readers can deduce all the major theorems in surface Ricci flow by themselves. The authors adapt the Ricci flow theory to practical computational algorithms, apply Ricci flow for shape analysis and surface registration, and demonstrate the power of Ricci flow in many applications in medical imaging, computer graphics, computer vision and wireless sensor network. Due to minimal pre-requisites, this book is accessible to engineers and medical experts, including educators, researchers, students and industry engineers who have an interest in solving real problems related to shape analysis and surface registration.
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admissible metric space Algorithm auxiliary metric Beltrami coefficient circle domain circle packing circle packing metric closed surfaces compute conformal factor conformal mapping conformal module conformal structure convex cosÂ cosh cosine law defined Definition denoted diffeomorphism discrete conformal discrete Ricci energy discrete surface Ricci edge lengths embedded Euclidean Ricci flow face surface function Gauss curvature geodesic curvature harmonic map Hessian matrix high genus surfaces homeomorphism human facial hyperbolic Ricci flow intersection angles isometric isothermal coordinates Lemma manifold mapping f mapping space mean curvature metric surfaces Möbius transformation Œvi vj vk planar plane preserving Proof quadratic differential quasi-conformal mapping Riemann mapping Riemann surface Riemannian metric rigid motion shape analysis shape space shown in Fig sinh Suppose surface registration surface Ricci flow surfaces with boundaries Teichmüller map Teichmüller space Theorem topological disk transformation group triangle triangular mesh unique vertex vertices Yamabe flow Zeng